The Frenet Serret Description of Gyroscopic Precession

The phenomenon of gyroscopic precession is studied within the framework of Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to the congruence vorticity is highlighted with particular reference to the irrotational congruence admitted by the stationary, axisymmetric spacetime. General precession formulae are obtained for circular orbits with arbitrary constant angular speeds. By successive reduction, different types of precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime family. The phenomenon is studied in the case of other interesting spacetimes, such as the De Sitter and G\"{o}del universes as well as the general stationary, cylindrical, vacuum spacetimes.Comment: 37 pages, Paper in Late

An error diffusion based method to generate functionally graded cellular structures

The spatial variation of cell size in a functionally graded cellular structure is achieved using error diffusion to convert a continuous tone image into binary form. Effects of two control parameters, greyscale value and resolution on the resulting cell size measures were investigated. Variation in cell edge length was greatest for the Voronoi connection scheme, particularly at certain parameter combinations. Relationships between these parameters and cell size were identified and applied to an example, where the target was to control the minimum and maximum cell size. In both cases there was an 8% underestimation of cell area for target regions

Computer simulation of recrystallization--III. Influence of a dispersion of fine particles

Two-dimensional Monte Carlo simulations of recrystallization have been carried out in the presence of incoherent and immobile particles for a range of different particle fractions, a range of stored energies and a range of densities of potential nuclei (embryos). For stored energies greater than a critical value (H/J > 1) the recrystallization front can readily pass the particles leading to a random density of particles on the front and a negligible influence of particles on the recrystallization kinetics. At lower stored energies the particles pin the recrystallization front leading to incomplete recrystallization. However at very low particle fractions, when the new grain has grown much larger than the matrix grains, before meeting any particles, the new grains can complete the consumption of the deformed grains giving complete "recrystallization" by a process that appears to be similar to abnormal grain growth. Particles are, as reported previously, very effective at pinning grain boundaries, both of the deformed and recrystallized grains, when boundaries migrate under essentially the driving force of boundary energy alone. Such boundaries show a density of particles that rises rapidly from the random value found at the start of the simulation. As a consequence, particles very strongly inhibit normal grain growth after recrystallization. Such growth can only occur if the as-recrystallized grain size is less than the limiting grain size seen in the absence of recrystallization. Under these circumstances a small increment of grain growth occurs until the grain boundaries once again acquire a higher than random density of particles.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29718/1/0000052.pd

A mechanical property evaluation of graded density Al-Si10-Mg lattice structures manufactured by selective laser melting

Metal components with applications across a range of industrial sectors can be manufactured by selective laser melting (SLM). A particular strength of SLM is its ability to manufacture components incorporating periodic lattice structures not realisable by conventional manufacturing processes. This enables the production of advanced, functionally graded, components. However, for these designs to be successful, the relationships between lattice geometry and performance must be established. We do so here by examining the mechanical behaviour of uniform and graded density SLM Al-Si10-Mg lattices under quasistatic loading. As-built lattices underwent brittle collapse and non-ideal deformation behaviour. The application of a microstructure-altering thermal treatment drastically improved their behaviour and their capability for energy absorption. Heat-treated graded lattices exhibited progressive layer collapse and incremental strengthening. Graded and uniform structures absorbed almost the same amount of energy prior to densification, 6.3±0.26.3±0.2 MJ/m3 and 5.7±0.25.7±0.2 MJ/m3, respectively, but densification occurred at around 7% lower strain for the graded structures. Several characteristic properties of SLM aluminium lattices, including their effective elastic modulus and Gibson-Ashby coefficients, C1 and α, were determined; these can form the basis of new design methodologies for superior components in the future

Mechanical properties of Ti-6Al-4V selectively laser melted parts with body-centred-cubic lattices of varying cell size

Significant weight savings in parts can be made through the use of additive manufacture (AM), a process which enables the construction of more complex geometries, such as functionally graded lattices, than can be achieved conventionally. The existing framework describing the mechanical properties of lattices places strong emphasis on one property, the relative density of the repeating cells, but there are other properties to consider if lattices are to be used effectively. In this work, we explore the effects of cell size and number of cells, attempting to construct more complete models for the mechanical performance of lattices. This was achieved by examining the modulus and ultimate tensile strength of latticed tensile specimens with a range of unit cell sizes and fixed relative density. Understanding how these mechanical properties depend upon the lattice design variables is crucial for the development of design tools, such as finite element methods, that deliver the best performance from AM latticed parts. We observed significant reductions in modulus and strength with increasing cell size, and these reductions cannot be explained by increasing strut porosity as has previously been suggested. We obtained power law relationships for the mechanical properties of the latticed specimens as a function of cell size, which are similar in form to the existing laws for the relative density dependence. These can be used to predict the properties of latticed column structures comprised of body-centred-cubic (BCC) cells, and may also be adapted for other part geometries. In addition, we propose a novel way to analyse the tensile modulus data, which considers a relative lattice cell size rather than an absolute size. This may lead to more general models for the mechanical properties of lattice structures, applicable to parts of varying size

Gaussian Process Modelling for Uncertainty Quantification in Convectively-Enhanced Dissolution Processes in Porous Media

Numerical groundwater flow and dissolution models of physico-chemical processes in deep aquifers are usually subject to uncertainty in one or more of the model input parameters. This uncertainty is propagated through the equations and needs to be quantified and characterised in order to rely on the model outputs. In this paper we present a Gaussian process emulation method as a tool for performing uncertainty quantification in mathematical models for convection and dissolution processes in porous media. One of the advantages of this method is its ability to significantly reduce the computational cost of an uncertainty analysis, while yielding accurate results, compared to classical Monte Carlo methods. We apply the methodology to a model of convectively-enhanced dissolution processes occurring during carbon capture and storage. In this model, the Gaussian process methodology fails due to the presence of multiple branches of solutions emanating from a bifurcation point, i.e., two equilibrium states exist rather than one. To overcome this issue we use a classifier as a precursor to the Gaussian process emulation, after which we are able to successfully perform a full uncertainty analysis in the vicinity of the bifurcation point

Systematic Reviews of Animal Experiments Demonstrate Poor Human Clinical and Toxicological Utility

The assumption that animal models are reasonably predictive of human outcomes provides the basis for their widespread use in toxicity testing and in biomedical research aimed at developing cures for human diseases. To investigate the validity of this assumption, the comprehensive Scopus biomedical bibliographic databases were searched for published systematic reviews of the human clinical or toxicological utility of animal experiments. In 20 reviews in which clinical utility was examined, the authors concluded that animal models were either significantly useful in contributing to the development of clinical interventions, or were substantially consistent with clinical outcomes, in only two cases, one of which was contentious. These included reviews of the clinical utility of experiments expected by ethics committees to lead to medical advances, of highly-cited experiments published in major journals, and of chimpanzee experiments — those involving the species considered most likely to be predictive of human outcomes. Seven additional reviews failed to clearly demonstrate utility in predicting human toxicological outcomes, such as carcinogenicity and teratogenicity. Consequently, animal data may not generally be assumed to be substantially useful for these purposes. Possible causes include interspecies differences, the distortion of outcomes arising from experimental environments and protocols, and the poor methodological quality of many animal experiments, which was evident in at least 11 reviews. No reviews existed in which the majority of animal experiments were of good methodological quality. Whilst the effects of some of these problems might be minimised with concerted effort (given their widespread prevalence), the limitations resulting from interspecies differences are likely to be technically and theoretically impossible to overcome. Non-animal models are generally required to pass formal scientific validation prior to their regulatory acceptance. In contrast, animal models are simply assumed to be predictive of human outcomes. These results demonstrate the invalidity of such assumptions. The consistent application of formal validation studies to all test models is clearly warranted, regardless of their animal, non-animal, historical, contemporary or possible future status. Likely benefits would include, the greater selection of models truly predictive of human outcomes, increased safety of people exposed to chemicals that have passed toxicity tests, increased efficiency during the development of human pharmaceuticals and other therapeutic interventions, and decreased wastage of animal, personnel and financial resources. The poor human clinical and toxicological utility of most animal models for which data exists, in conjunction with their generally substantial animal welfare and economic costs, justify a ban on animal models lacking scientific data clearly establishing their human predictivity or utility

A measurement of the tau mass and the first CPT test with tau leptons

We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV using tau pairs from Z0 decays. To test CPT invariance we compare the masses of the positively and negatively charged tau leptons. The relative mass difference is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.

Measurement of the B0 Lifetime and Oscillation Frequency using B0->D*+l-v decays

The lifetime and oscillation frequency of the B0 meson has been measured using B0->D*+l-v decays recorded on the Z0 peak with the OPAL detector at LEP. The D*+ -> D0pi+ decays were reconstructed using an inclusive technique and the production flavour of the B0 mesons was determined using a combination of tags from the rest of the event. The results t_B0 = 1.541 +- 0.028 +- 0.023 ps, Dm_d = 0.497 +- 0.024 +- 0.025 ps-1 were obtained, where in each case the first error is statistical and the second systematic.Comment: 17 pages, 4 figures, submitted to Phys. Lett.

First Measurement of Z/gamma* Production in Compton Scattering of Quasi-real Photons

We report the first observation of Z/gamma* production in Compton scattering of quasi-real photons. This is a subprocess of the reaction e+e- to e+e-Z/gamma*, where one of the final state electrons is undetected. Approximately 55 pb-1 of data collected in the year 1997 at an e+e- centre-of-mass energy of 183 GeV with the OPAL detector at LEP have been analysed. The Z/gamma* from Compton scattering has been detected in the hadronic decay channel. Within well defined kinematic bounds, we measure the product of cross-section and Z/gamma* branching ratio to hadrons to be (0.9+-0.3+-0.1) pb for events with a hadronic mass larger than 60 GeV, dominated by (e)eZ production. In the hadronic mass region between 5 GeV and 60 GeV, dominated by (e)egamma* production, this product is found to be (4.1+-1.6+-0.6) pb. Our results agree with the predictions of two Monte Carlo event generators, grc4f and PYTHIA.Comment: 18 pages, LaTeX, 5 eps figures included, submitted to Physics Letters